Question

Which of the following polynomials does not have real roots?

A. -x2 + 4x + 6
B. x2 - 17x - 7
C. x2 + 4x + 8
D. 2x2 - 13

Answer 1

is it D ?

Answer 2

I guess for each of these, you should just worry about the `descriminant`.
When given: \(\large\rm ax^2+bx+c\)

Solutions of x are given by:\[\large\rm x=\frac{-b\pm\sqrt{\color{orangered}{b^2-4ac}}}{2a}\]We really only care about this orange part,
when it's negative, we have no real solutions.

Answer 3

Let's look at D a sec,
It has this form:\[\large\rm 2x^2+0x-13\]No x's, so I put a placeholder to show what my b coefficient is.

Answer 4

\[\large\rm b^2-4ac\quad=0^2-4(2)(-13)\]D turns out to be a `positive` number, ya?

Answer 5

so it would be B

Answer 6

or A

Answer 7

because you said it would have to be positive

Answer 8

Option A:\[\large\rm -1x^2+4x+6\]gives,\[\large\rm b^2-4ac\quad=(-1)^2-4(4)(6)\]


Option B:\[\large\rm 1x^2 - 17x - 7\]gives,\[\large\rm b^2-4ac\quad=(-17)^2-4(1)(-7)\]

Answer 9

Yes, it has to be negative result to give us the answer we're looking for.
Which one is that? :)

Answer 10

positive discriminant = real roots

We're looking for this situation:
negative discriminant = no real roots

Answer 11

so is it A ? because gives me a positive answer

Answer 12

A gives you a positive? Are you sure?\[\large\rm b^2-4ac\quad=(-1)^2-4(4)(6)\quad= 1-96\quad= -95\]

Answer 13

i meant to put b for the positive answer

Answer 14

We were looking for the `negative` though,
so yes option A :)

Answer 15

thank you , (: